It doesn't matter if you have any other information on the security of the algorithm; the fact that they're offering you money should speak for itself.
It's in the best interests of national security for the NSA to promote both good and/or backdoored algorithms for all allied nations and their corporations.
The public cryptographic community started brute-forcing DES keys for fun in the '90s; with the NSA's budget, they could have been doing it from the beginning.
* DES keys are 64 bits, but 8 bits are for parity, so the meaningful key length is 56 bits.
It makes sense if you think about it: Both goals are useful to Uncle Sam and both require the same skill set. The trouble is it obviously creates quite the conflict of interest.
While a separate organisation might be best, even a division within NSA etc. explicitly tasked with protection rather than intelligence gathering would be preferable to the status quo, so long as its head could be publically known. In the end it comes down to there being no individual with that responsibility. You need someone who is visible in that role, whose mission is purely to protect, overseeing a staff whose mission is purely to protect.
What am I missing?